1. Field of the Invention
The present invention relates to image signal transforming method, image signal inversely-transforming method, image encoding apparatus, image encoding method, image encoding program, image decoding apparatus, image decoding method, and image decoding program.
2. Related Background Art
Conventionally, the compressive coding techniques are used for efficiently performing transmission and storage of still image and moving image data. Particularly, MPEG (Moving Picture Experts Group) 1, 2, and 4 and H.261-H.264 systems are used in the case of moving images, and JPEG (Joint Photographic Experts Group) and JPEG2000 are used in the case of still images.
In most of these coding systems, an image as an object for coding is decomposed into a plurality of blocks and the discrete cosine transform (hereinafter referred to as “DCT”) is applied to transform each block itself or a differential signal between the block and a prediction signal for the block, into data in the frequency domain. The transformation coefficients obtained by the transformation are quantized to compress the data volume of the signal of the original image. In reconstruction, the compressed data is dequantized into a signal of each block, and the inverse discrete cosine transform (hereinafter referred to as “IDCT”) is applied to restore a signal or differential signal in the pixel domain. The coding using DCT is described, for example, in U.S. Pat. No. 5,196,946.
FIG. 1 is a block diagram showing the DCT process according to the conventional technology. This example corresponds to a case where four pixels are transformed into data in the frequency domain. Four pixels a0, a1, a2, and a3 are supplied via respective input terminals 101-104. Adder 113 adds a0 and a3 and subtractor 114 obtains a difference between a0 and a3. Similarly, a1 and a2 are processed by adder 115 and subtractor 116. These results are fed via respective terminals 105-108 to the next stage. The signals from terminals 105 and 106 are processed by adder 117 and subtractor 118, and the signals from terminals 107 and 108 by adder 119, subtractor 120, and multipliers 121 and 122. Results obtained in this manner are coefficients in the frequency domain and outputted via terminals 109-112.
FIG. 2 is a block diagram showing the IDCT process according to the conventional technology. Coefficients in the frequency domain are imported via respective input terminals 201-204. The coefficients from terminals 201 and 202 are processed by adder 213 and subtractor 214, and the coefficients from terminals 203 and 204 by subtractor 215, adder 216, and multipliers 221 and 222. Signals obtained in this manner are fed via terminals 205-208 to the next stage. The signals from terminals 205 and 208 are processed by adder 217 and subtractor 218, and the signals from terminals 206 and 207 by adder 219 and subtractor 220. In this manner the coefficients in the frequency domain are inversely transformed into the original pixels a0, a1, a2, and a3 and they are outputted from respective terminals 209-212.
As described above, the encoding apparatus is able to express an input signal in a compact form through the transformation of the image into the frequency domain and thus to achieve efficient coding.